True. Though misandry also includes the devaluing of certain ways a masculine identifying person might express that masculinity, just as misogyny also includes ways the devaluing of certain ways a feminine identifying person might express their femininity. Misandry is not simply the wholesale hatred of men and/or masculinity, just as misogyny is not simply the wholesale hatred of women and/or femininity. Toxic masculinity, as a term, encompasses behaviours which are driven by misogyny, misandry, and the, in masculine people, internalised misandry resulting in the perpetuation of mysogyny and misandrist attitudes.
To see it as caused solely by internalised misandry is limiting. Such a view ignores the fact that toxic masculinity is a gestalt of behaviours driven by many different beliefs and attitudes - it ignores the fact that toxic masculinity is exhibited when mysogynistic or misandrisric behaviours are observed, and the observer is coerced by society to act in that manner thus perpetuating the cycle of sexism, internalised or not.
If we want to address the syndrome we call toxic masculinity, we'll need to dissect it thoroughly. We'll need to name and target each component. As it is composed of behaviours resulting from all forms of sexism, we must address all those named forms of sexism in society from all applicable sources. Everyone in society contributes to toxic masculinity - but in different ways. Clearly a multifaceted approach is required - one in which we must all participate actively.
Sexism is unacceptable and the mechanisms by which sexism perpetuates itself must be destroyed. Language is a very powerful weapon in that fight. We have a direct responsibility to use it effectively and with great precision. Let's carefully examine the words we use in this struggle to eliminate what we call toxic masculinity, because clearly there's some real confusion about what we're talking about here and some debate about who needs take action - because we all need to take action.